...It seems to me that we should begin to engage in this activity independent of politics or protests...

Why? What purpose supportive of the RKBA would it serve? Why would you think it would serve that purpose? Any evidence or data to support your beliefs?

It strikes me that many people who support gun control and politicians who vote for gun control legislation do so because they are frightened of people who own guns. I don't see how a sort of demonstration as suggested by the OP could ameliorate those fears, and would more likely to increase them.

In any case, what positive would likely come of this sort of exercise?

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"It is long been a principle of ours that one is no more armed because he has possession of a firearm than he is a musician because he owns a piano. There is no point in having a gun if you are not capable of using it skillfully." -- Jeff Cooper